Pareto-optimal reinsurance design in a duopoly market with asymmetric information

Haonan Ma; Ying Fang; Haonan Ma; Ying Fang

doi:10.3934/math.2025826

AIMS Mathematics

2025, Volume 10, Issue 8: 18494-18523. doi: 10.3934/math.2025826

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Research article

Pareto-optimal reinsurance design in a duopoly market with asymmetric information

Haonan Ma ,
Ying Fang ^,

School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, China

Received: 02 July 2025 Revised: 04 August 2025 Accepted: 11 August 2025 Published: 15 August 2025
MSC : 91G05, 91G30

This work studied the optimal reinsurance design in a duopolistic market comprising two types of insurers and two reinsurers under asymmetric information, where reinsurers cannot directly observe insurers' risk types. We modeled reinsurers as risk-neutral agents maximizing expected net profit, subject to individual rationality, incentive compatibility, and convex preference constraints. We introduced the principle of Pareto optimality to formulate the objective function in a multi-agent setting. Applying the Lagrange dual approach, we derived optimal reinsurance menus for all cases. Under the Value-at-Risk (VaR) risk measure, we identified the globally optimal reinsurance menu by comparative analysis and provided its closed-form solution. Furthermore, we compared exponential and Pareto distributions with identical expected losses to study tail risk effects.
- Pareto-optimal reinsurance,
- asymmetric information,
- duopolistic market,
- distortion risk measures,
- individual rationality,
- incentive compatibility,
- convex preference
Citation: Haonan Ma, Ying Fang. Pareto-optimal reinsurance design in a duopoly market with asymmetric information[J]. AIMS Mathematics, 2025, 10(8): 18494-18523. doi: 10.3934/math.2025826

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Abstract

This work studied the optimal reinsurance design in a duopolistic market comprising two types of insurers and two reinsurers under asymmetric information, where reinsurers cannot directly observe insurers' risk types. We modeled reinsurers as risk-neutral agents maximizing expected net profit, subject to individual rationality, incentive compatibility, and convex preference constraints. We introduced the principle of Pareto optimality to formulate the objective function in a multi-agent setting. Applying the Lagrange dual approach, we derived optimal reinsurance menus for all cases. Under the Value-at-Risk (VaR) risk measure, we identified the globally optimal reinsurance menu by comparative analysis and provided its closed-form solution. Furthermore, we compared exponential and Pareto distributions with identical expected losses to study tail risk effects.

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